Question: How many distinct three-digit numbers can be written with the digits $1$, $2$, $3$ and $4$ if no digit may be used more than once in a three-digit number?
Explanation: There are 4 choices for which number can be in the hundreds place.  For each possibility, there are 3 choices remaining for which number can be in the tens place, leaving 2 choices for the units place.  This gives a total of $4\cdot 3\cdot 2 = \boxed{24}$ possible three-digit numbers.